Prior Content: Solving Simple Equations, Substitution, Surds, Factorising
Possible Next Steps: Quadratic Inequalities, Simultaneous Equations, Drawing & Using Graphs, Completing the Square, Differentiation, Sequences, Algebraic Proof, Algebraic Fractions, Circle Theorems, Functions
Contents
- 1.1 The Zero-Product Principle
- 1.2 Using Pre-Factorised Expressions to Solve Equations
- 1.3 Solving Quadratics by Factorising (Including Rearranging)
- 2.1 Solving Quadratics Using the Quadratic Formula
- 2.2 The Discriminant & Numbers of Real Solutions
- 3.1 Quadratics in Context
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 The Zero-Product Principle
Teaching Videos, Exercises & Activities
Tutorial Videos
Solving equations with zero product property by Khan Academy
Zero Product Property by The Organic Chemistry Tutor
Zero Product Property How to Use by Mario's Math Tutoring
Online Platforms (with Videos & Exercises)
- Khan Academy
- Quadratics in factorised form: Videos & practice
Activities & Resources
Worksheets
Dr Frost Resources
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
No Key Skills Yet
Extension Materials
1.2 Using Pre-Factorised Expressions to Solve Equations
Teaching Videos, Exercises & Activities
Tutorial Videos
Solving Quadratic Equations by Factorising (Non-Calculator) by The GCSE Maths Tutor
Solving Quadratics by Factoring by Professor Dave Explains
Online Platforms (with Videos & Exercises)
Activities & Resources
- BossMaths
Worksheets
Dr Frost Resources
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
Extension Materials
1.3 Solving Quadratics by Factorising (Including Rearranging)
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Solving Quadratics Using Factorisation
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
- Solving Quadratic Equations ppt (Slides 1-20)
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- Acute Learning Problem Pairs
- Level 2 FM: Solving Linear & Quadratic Equations as PowerPoint or PDF
- Interactive Maths
- Solving Quadratics by Factorising: Factorising Tool | Video
- Go Teach Maths
- Solving Quadratic Equations Using Factorisation: Without Coefficients
- Solving Quadratic Equations Using Factorisation: With Coefficients
- Solving Quadratic Equations by Rearranging When b = 0
- Solving Quadratic Equations Using the Difference of Two Squares
- Solving Quadratic Equations When b = 0
- Solving Quadratic Equations by Rearranging When c = 0
- Dan Walker
- Mr Thompson Maths
- Chritsopher
- Ticktock Maths
Worksheets
- Dr Austin Maths
- Practice Strips (Word | PDF | Answers)
- Match-Up (Word | PDF✦ | Answers✦)
- Harder by Factorising Practice Strips (Word | PDF | Answers)
- Equations Revision Practice Grid ((Editable Word | PDF | Answers)
- Fill in the Blanks (Word | PDF | Answers)
- Crack the Code (Word | PDF | Answers)
- Which Require Rearrangement Practice Strips (Word | PDF | Answers)
- Harder by Factorising Name the Film (Word | PDF | Answers)
- Sort It Out (Word | PDF | Answers)
- Corbettmaths
- Maths 4 Everyone
- Pixi Maths
- Mathshelper (Jon Stone)
- Quadratic Equations 1 · 2
- Quadratic Factorisation & Solving Worksheet
- Solving Quadratics
- Maths Genie
- Solving Quadratics: Booklet · Worksheet · Solutions · Lesson · Topic page
- Naiker Maths
- Solving Quadratics by Factorisation: Worksheet
- crashMATHS
- Access Maths
- MME
- Dr Frost
- MadAsMaths (T. Madas)
- Starting Points Maths
- Mr Morley Maths
- Solving Quadratic Equations (Factorise and Quadratic Formula): Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (@MathedUp)
- Solving Quadratics by Factorising (@MathedUp, pptx)
- Pret Homework (A Dai)
- Solving Quadratics by Factorising (A Dai, docx)
Dr Frost resources
Dr Frost Video
K615: Solve Quadratics of the Form x2+bx+c=0, Solvable by Factorisation.
K618: Solve Quadratics of the Form ax2+bx+c=0, Requiring Rearrangement and Factorising.
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 367b: Solve quadratic equations given in the form x2 ± bx ± c = 0, solvable by factorisation.
- 367c: Solve quadratic equations requiring rearrangement to the form x2 ± bx ± c = 0 by factorising.
- 367d: Solve quadratic equations given in the form ax2 ± bx ± c = 0, requiring factorising.
- 367e: Solve quadratic equations requiring rearrangement to the form ax2 ± bx ± c = 0 by factorising.
- 367f: Solve a quadratic equation of the form x2-a2=0 or x2=a2 by factorisation.
- 367g: Solve a quadratic equation of the form ax2-b2=0 or ax2=b2 by factorisation.
- 367h: Determine the original quadratic equation given its integer solutions.
- 367i: Determine the original quadratic equation given its non-integer solutions.
- 500a: Solve cubic equations given in the form x3 + bx2 + cx = 0, solvable by factorisation.
- 500b: Solve cubic equations given in the form ax3 + bx2 + cx = 0, solvable by factorisation.
- 367: Exam Practice: Solving quadratic equations by factorisation
- 500: Exam Practice: Solving cubic equations
Further Practice
- Practise Questions (may include angles in a triangle and on a straight line)
EXTENSION MATERIALS
Videos & Other Multimedia
Quadratic to the power of Quadratic 🤯 || The Devil’s Equation. 😈 by Curiosity Squared
Online Platforms
- Khan Academy
- Solving quadratics by factorising: Videos & practice
2.1 Solving Quadratics Using the Quadratic Formula
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Quadratic Formula
Online Platforms (with Videos & Exercises)
- Khan Academy
- The quadratic formula & discriminant: Videos & practice
Activities
- Pixi Maths
- Solving Quadratic Equations ppt (Slides 21-33)
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Mrs Newell
- Don Steward
- Interactive Maths
- The Quadratic Formula: Video
- Mr Draper Maths Using the Quadratic Formula: Homework
- Go Teach Maths
- Open Middle
- Lawrence Houldsworth
- Ticktock Maths
Worksheets
- Andy Lutwyche
- Dr Austin Maths
- Mathshelper (Jon Stone)
- Maths Genie
- Quadratic Formula: Booklet · Worksheet · Solutions · Lesson · Topic page
- crashMATHS
- MME
- 1st Class Maths
- MadAsMaths (T. Madas)
- Quadratics Exam Questions Q1 (difficulty 2 of 5)
- timcw
- Pret Homework (Jo Morgan)
- Quadratic Formula✦ (Jo Morgan, docx)
- Dr Austin Maths
- Corbettmaths
- Quadratic Formula Practice Questions & Solutions
- Quadratic Formula Worksheet & Solutions
- Quadratics Formula (AQA Level 2) Practice Questions & Solutions
- Maths 4 Everyone
- Pixi Maths
Dr Frost resources
Dr Frost Video
K619: Solve a Quadratic Equation to Get Exact Solutions.
K620: Solve a Quadratic Equation Using the Formula or Completing the Square to Get Numerical Solutions.
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 417a: Solve a quadratic equation using the quadratic formula to get exact solutions.
- 417b: Solve a quadratic equation using the quadratic formula to get numeric solutions.
- 417c: Solve quadratic equations using the quadratic formula, requiring rearrangement.
- 417d: Determine the original quadratic equation given use of the quadratic formula.
- 417: Exam Practice: Quadratic formula to solve quadratic equations
Further Practice
- Practise Questions
EXTENSION MATERIALS
2.2 The Discriminant & Numbers of Real Solutions
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
The Discriminant | Algebra | GCSE Further Maths | A-Level Maths Series by The GCSE Maths Tutor
The Discriminant – Corbettmaths by corbettmaths
A-Level Maths: B3-17 [Quadratics: Using the Discriminant to Find How Many Roots a Quadratic Has] by TLMaths
Edexcel AS Level Maths : 2.5 The Discriminant by Zeeshan Zamurred
Online Platforms (with Videos & Exercises)
Activities
- Math = Love (Sarah Carter)
- Go Teach Maths
Worksheets
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 492a: Calculate the discriminant of a quadratic function with numeric coefficients.
- 492b: Use the discriminant of a simple quadratic function to determine the number of solutions to an equation.
- 492c: Understand the relationship between the discriminant of a quadratic function and its sketch.
- 492d: Determine the discriminant of a quadratic function with algebraic coefficients.
- 492e: Use the discriminant to reason about the number of solutions of a factorised cubic.
- 492f: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, where there are equal roots.
- 492g: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, where there are no roots or distinct roots.
- 492h: Use the discriminant to determine the values for algebraic coefficients in a quadratic function, requiring rearrangement.
- 492i: Use the discriminant to determine when a straight line is tangent to a quadratic graph.
- 492j: Prove that a quadratic with algebraic coefficients always has either distinct or no solutions.
- 492: Exam Practice: Discriminant of a quadratic function
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.1 Quadratics in Context
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities
- Andy Lutwyche
- Don Steward
- The Chalkface
- FlightPath: Excel (if macros are blocked: right-click the file › Properties › tick Unblock)
- Transum
- Interactive Maths
- Problems Involving Quadratic Equations: Video
- Go Teach Maths
- Desmos
- Will It Hit the Hoop? (model basketball shots with parabolas)
- pas1001
- Ticktock Maths
Worksheets
- Dr Austin Maths
- Mathsaurus (Kevin Olding)
- MadAsMaths (T. Madas)
- Equations Exam Questions I Q46 (difficulty 4 of 5)
- Quadratics Exam Questions Q60, 75, 77 (difficulty 3–4 of 5)
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- Slides & Worksheet
Topic Test
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 418a: Form (and solve) a quadratic equation or expression from the area of a rectangle.
- 418b: Form (and solve) a quadratic equation or expression using sides of a right-angled triangle where the area is known.
- 418c: Form (and solve) a quadratic equation or expression from the area of a more complex rectilinear shape.
- 418d: Form (and solve) a quadratic equation or expression from the area of a trapezium.
- 418e: Form (and solve) a quadratic equation or expression for the area of a trapezium inside a rectangle.
- 418f: Form (and solve) a quadratic equation or expression by equating the area of two shapes.
- 418g: Form (and solve) a quadratic equation or expression using the sides of a right-angled triangle using Pythagoras’ Theorem.
- 418h: Form (and solve) a quadratic equation or expression using sides of a right-angled triangle where the perimeter is known.
- 418i: Form (and solve) a quadratic equation or expression using the dimensions of a cuboid where the volume is known or where two volumes are equal.
- 418j: Form (and solve) a quadratic equation or expression using the dimensions of a cuboid where the surface area is known.
- 418k: Form (and solve) a quadratic equation or expression using the dimensions of a prism where the volume is known.
- 418l: Form (and solve) a quadratic equation or expression to determine the radius or diameter of a cylinder given its surface area.
- 418m: Form (and solve) a quadratic equation or expression to determine an unknown dimension of a semi-cylinder given its surface area.
- 418n: Form (and solve) a quadratic equation or expression using the dimensions of a cone where the surface area is known.
- 418o: Form (and solve) a quadratic equation or expression for the volume of a cuboid given its net.
- 418p: Write a non-linear expression in one variable by rearranging known relationships between two variables.
- 418: Exam Practice: Forming and solving quadratic or non-linear expressions or equations from a given context (excluding probability problems)
Further Practice
- Practise Questions
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Solving Quadratics PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Solving Equations (Cubic + Other) as PowerPoint or PDF
- Solving Equations (Quadratic) as PowerPoint or PDF
- Solving Equations (Quadratics Hidden) as PowerPoint or PDF
- Solving Equations (With Squares) as PowerPoint or PDF
Worksheets
- Maths 4 Everyone
- Andy Lutwyche
- Mathshelper (Jon Stone)
- MathedUp
- Solving Quadratics by Factorising: Worksheet · Practice · Quiz · Question Gallery
- Harder Quadratics (a ≠ 1): Worksheet · Practice · Quiz · Question Gallery
- The Quadratic Formula: Worksheet · Practice · Quiz · Question Gallery
- Solving Quadratics: Worksheet · Practice · Quiz · Question Gallery
- Mathsaurus (Kevin Olding)
- Physics & Maths Tutor
- Interwoven Maths
- crashMATHS
Activities
- Intervention Tasks
- NRICH (student problems)
- Don Steward
- The Chalkface
- Quadratic Powers Problem: PDF
- Transum
- Interactive Maths
- Solving Quadratic Equations: QQI | 10QQI | Count Down | Relay | Bingo
- Solving Quadratic Equations: Worksheets
- Go Teach Maths
- MathsPad
- Desmos
- @DrStoneMaths
- Dr Austin Maths
External
- crashMATHS
- NCETM
External Whole Topic Past Paper Style Questions
- Transum
- Exam-style questions: Quadratic Equations
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.